Theorem 7.11 [1]}, [2]}
Let \(\eta :\Lambda \xrightarrow{}\Lambda \)  be a derivation. Let \(\mathbb {K}\)  be a projective resolution of \(\Lambda \)  as a \(\Lambda ^e\) -module. Let \(\chi \in \operatorname{Hom}_{\Lambda ^e}(\mathbb {K}_n,\Lambda )\)  be a cocycle and let \(\tilde{\eta }_{n}:\mathbb {K}_{n}\xrightarrow{}\mathbb {K}_{n}\)  be derivation operators satisfying Equation (REF ). The Gerstenhaber bracket of \(\eta \)  and \(\chi \)  is represented by
\([\eta ,\chi ] = \eta \chi - \chi \tilde{\eta }_n\) 
